Properties

Label 35.5.g.a.22.12
Level $35$
Weight $5$
Character 35.22
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,5,Mod(8,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.8");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.12
Character \(\chi\) \(=\) 35.22
Dual form 35.5.g.a.8.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.12784 + 5.12784i) q^{2} +(10.3372 - 10.3372i) q^{3} +36.5894i q^{4} +(-22.2980 - 11.3048i) q^{5} +106.015 q^{6} +(13.0958 + 13.0958i) q^{7} +(-105.579 + 105.579i) q^{8} -132.716i q^{9} +O(q^{10})\) \(q+(5.12784 + 5.12784i) q^{2} +(10.3372 - 10.3372i) q^{3} +36.5894i q^{4} +(-22.2980 - 11.3048i) q^{5} +106.015 q^{6} +(13.0958 + 13.0958i) q^{7} +(-105.579 + 105.579i) q^{8} -132.716i q^{9} +(-56.3718 - 172.310i) q^{10} -135.891 q^{11} +(378.233 + 378.233i) q^{12} +(-35.4752 + 35.4752i) q^{13} +134.306i q^{14} +(-347.360 + 113.640i) q^{15} -497.356 q^{16} +(146.269 + 146.269i) q^{17} +(680.549 - 680.549i) q^{18} -408.482i q^{19} +(413.634 - 815.873i) q^{20} +270.749 q^{21} +(-696.826 - 696.826i) q^{22} +(212.278 - 212.278i) q^{23} +2182.79i q^{24} +(369.405 + 504.148i) q^{25} -363.822 q^{26} +(-534.605 - 534.605i) q^{27} +(-479.168 + 479.168i) q^{28} +195.559i q^{29} +(-2363.93 - 1198.48i) q^{30} +965.178 q^{31} +(-861.090 - 861.090i) q^{32} +(-1404.73 + 1404.73i) q^{33} +1500.08i q^{34} +(-143.966 - 440.055i) q^{35} +4856.02 q^{36} +(925.201 + 925.201i) q^{37} +(2094.63 - 2094.63i) q^{38} +733.431i q^{39} +(3547.76 - 1160.66i) q^{40} -2299.21 q^{41} +(1388.35 + 1388.35i) q^{42} +(-1190.20 + 1190.20i) q^{43} -4972.17i q^{44} +(-1500.33 + 2959.32i) q^{45} +2177.05 q^{46} +(-1550.35 - 1550.35i) q^{47} +(-5141.28 + 5141.28i) q^{48} +343.000i q^{49} +(-690.938 + 4479.44i) q^{50} +3024.03 q^{51} +(-1298.02 - 1298.02i) q^{52} +(645.219 - 645.219i) q^{53} -5482.73i q^{54} +(3030.10 + 1536.21i) q^{55} -2765.29 q^{56} +(-4222.57 - 4222.57i) q^{57} +(-1002.79 + 1002.79i) q^{58} +2295.44i q^{59} +(-4158.03 - 12709.7i) q^{60} +3198.88 q^{61} +(4949.28 + 4949.28i) q^{62} +(1738.03 - 1738.03i) q^{63} -873.373i q^{64} +(1192.07 - 389.989i) q^{65} -14406.5 q^{66} +(-6113.48 - 6113.48i) q^{67} +(-5351.89 + 5351.89i) q^{68} -4388.73i q^{69} +(1518.30 - 2994.77i) q^{70} +740.397 q^{71} +(14012.1 + 14012.1i) q^{72} +(1763.21 - 1763.21i) q^{73} +9488.56i q^{74} +(9030.11 + 1392.86i) q^{75} +14946.1 q^{76} +(-1779.60 - 1779.60i) q^{77} +(-3760.91 + 3760.91i) q^{78} +8409.12i q^{79} +(11090.1 + 5622.48i) q^{80} -302.630 q^{81} +(-11790.0 - 11790.0i) q^{82} +(5894.49 - 5894.49i) q^{83} +9906.53i q^{84} +(-1607.97 - 4915.04i) q^{85} -12206.3 q^{86} +(2021.54 + 2021.54i) q^{87} +(14347.2 - 14347.2i) q^{88} -4763.09i q^{89} +(-22868.3 + 7481.47i) q^{90} -929.153 q^{91} +(7767.12 + 7767.12i) q^{92} +(9977.27 - 9977.27i) q^{93} -15899.8i q^{94} +(-4617.78 + 9108.34i) q^{95} -17802.6 q^{96} +(687.835 + 687.835i) q^{97} +(-1758.85 + 1758.85i) q^{98} +18034.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.12784 + 5.12784i 1.28196 + 1.28196i 0.939551 + 0.342408i \(0.111242\pi\)
0.342408 + 0.939551i \(0.388758\pi\)
\(3\) 10.3372 10.3372i 1.14858 1.14858i 0.161749 0.986832i \(-0.448287\pi\)
0.986832 0.161749i \(-0.0517134\pi\)
\(4\) 36.5894i 2.28684i
\(5\) −22.2980 11.3048i −0.891922 0.452190i
\(6\) 106.015 2.94487
\(7\) 13.0958 + 13.0958i 0.267261 + 0.267261i
\(8\) −105.579 + 105.579i −1.64968 + 1.64968i
\(9\) 132.716i 1.63848i
\(10\) −56.3718 172.310i −0.563718 1.72310i
\(11\) −135.891 −1.12306 −0.561532 0.827455i \(-0.689788\pi\)
−0.561532 + 0.827455i \(0.689788\pi\)
\(12\) 378.233 + 378.233i 2.62662 + 2.62662i
\(13\) −35.4752 + 35.4752i −0.209913 + 0.209913i −0.804230 0.594318i \(-0.797422\pi\)
0.594318 + 0.804230i \(0.297422\pi\)
\(14\) 134.306i 0.685236i
\(15\) −347.360 + 113.640i −1.54382 + 0.505067i
\(16\) −497.356 −1.94280
\(17\) 146.269 + 146.269i 0.506120 + 0.506120i 0.913333 0.407213i \(-0.133499\pi\)
−0.407213 + 0.913333i \(0.633499\pi\)
\(18\) 680.549 680.549i 2.10046 2.10046i
\(19\) 408.482i 1.13153i −0.824567 0.565764i \(-0.808581\pi\)
0.824567 0.565764i \(-0.191419\pi\)
\(20\) 413.634 815.873i 1.03409 2.03968i
\(21\) 270.749 0.613942
\(22\) −696.826 696.826i −1.43972 1.43972i
\(23\) 212.278 212.278i 0.401281 0.401281i −0.477403 0.878684i \(-0.658422\pi\)
0.878684 + 0.477403i \(0.158422\pi\)
\(24\) 2182.79i 3.78957i
\(25\) 369.405 + 504.148i 0.591048 + 0.806636i
\(26\) −363.822 −0.538199
\(27\) −534.605 534.605i −0.733340 0.733340i
\(28\) −479.168 + 479.168i −0.611184 + 0.611184i
\(29\) 195.559i 0.232531i 0.993218 + 0.116266i \(0.0370924\pi\)
−0.993218 + 0.116266i \(0.962908\pi\)
\(30\) −2363.93 1198.48i −2.62659 1.33164i
\(31\) 965.178 1.00435 0.502174 0.864767i \(-0.332534\pi\)
0.502174 + 0.864767i \(0.332534\pi\)
\(32\) −861.090 861.090i −0.840908 0.840908i
\(33\) −1404.73 + 1404.73i −1.28993 + 1.28993i
\(34\) 1500.08i 1.29765i
\(35\) −143.966 440.055i −0.117523 0.359229i
\(36\) 4856.02 3.74693
\(37\) 925.201 + 925.201i 0.675822 + 0.675822i 0.959052 0.283230i \(-0.0914059\pi\)
−0.283230 + 0.959052i \(0.591406\pi\)
\(38\) 2094.63 2094.63i 1.45057 1.45057i
\(39\) 733.431i 0.482203i
\(40\) 3547.76 1160.66i 2.21735 0.725414i
\(41\) −2299.21 −1.36776 −0.683881 0.729594i \(-0.739709\pi\)
−0.683881 + 0.729594i \(0.739709\pi\)
\(42\) 1388.35 + 1388.35i 0.787049 + 0.787049i
\(43\) −1190.20 + 1190.20i −0.643701 + 0.643701i −0.951463 0.307763i \(-0.900420\pi\)
0.307763 + 0.951463i \(0.400420\pi\)
\(44\) 4972.17i 2.56827i
\(45\) −1500.33 + 2959.32i −0.740902 + 1.46139i
\(46\) 2177.05 1.02885
\(47\) −1550.35 1550.35i −0.701832 0.701832i 0.262972 0.964804i \(-0.415297\pi\)
−0.964804 + 0.262972i \(0.915297\pi\)
\(48\) −5141.28 + 5141.28i −2.23146 + 2.23146i
\(49\) 343.000i 0.142857i
\(50\) −690.938 + 4479.44i −0.276375 + 1.79177i
\(51\) 3024.03 1.16264
\(52\) −1298.02 1298.02i −0.480036 0.480036i
\(53\) 645.219 645.219i 0.229697 0.229697i −0.582869 0.812566i \(-0.698070\pi\)
0.812566 + 0.582869i \(0.198070\pi\)
\(54\) 5482.73i 1.88022i
\(55\) 3030.10 + 1536.21i 1.00169 + 0.507839i
\(56\) −2765.29 −0.881789
\(57\) −4222.57 4222.57i −1.29965 1.29965i
\(58\) −1002.79 + 1002.79i −0.298096 + 0.298096i
\(59\) 2295.44i 0.659419i 0.944082 + 0.329710i \(0.106951\pi\)
−0.944082 + 0.329710i \(0.893049\pi\)
\(60\) −4158.03 12709.7i −1.15501 3.53047i
\(61\) 3198.88 0.859682 0.429841 0.902905i \(-0.358570\pi\)
0.429841 + 0.902905i \(0.358570\pi\)
\(62\) 4949.28 + 4949.28i 1.28753 + 1.28753i
\(63\) 1738.03 1738.03i 0.437901 0.437901i
\(64\) 873.373i 0.213226i
\(65\) 1192.07 389.989i 0.282146 0.0923052i
\(66\) −14406.5 −3.30728
\(67\) −6113.48 6113.48i −1.36188 1.36188i −0.871520 0.490360i \(-0.836865\pi\)
−0.490360 0.871520i \(-0.663135\pi\)
\(68\) −5351.89 + 5351.89i −1.15742 + 1.15742i
\(69\) 4388.73i 0.921808i
\(70\) 1518.30 2994.77i 0.309857 0.611177i
\(71\) 740.397 0.146875 0.0734375 0.997300i \(-0.476603\pi\)
0.0734375 + 0.997300i \(0.476603\pi\)
\(72\) 14012.1 + 14012.1i 2.70295 + 2.70295i
\(73\) 1763.21 1763.21i 0.330870 0.330870i −0.522047 0.852917i \(-0.674831\pi\)
0.852917 + 0.522047i \(0.174831\pi\)
\(74\) 9488.56i 1.73275i
\(75\) 9030.11 + 1392.86i 1.60535 + 0.247620i
\(76\) 14946.1 2.58762
\(77\) −1779.60 1779.60i −0.300152 0.300152i
\(78\) −3760.91 + 3760.91i −0.618165 + 0.618165i
\(79\) 8409.12i 1.34740i 0.739005 + 0.673700i \(0.235296\pi\)
−0.739005 + 0.673700i \(0.764704\pi\)
\(80\) 11090.1 + 5622.48i 1.73282 + 0.878513i
\(81\) −302.630 −0.0461256
\(82\) −11790.0 11790.0i −1.75342 1.75342i
\(83\) 5894.49 5894.49i 0.855637 0.855637i −0.135183 0.990821i \(-0.543162\pi\)
0.990821 + 0.135183i \(0.0431623\pi\)
\(84\) 9906.53i 1.40399i
\(85\) −1607.97 4915.04i −0.222557 0.680282i
\(86\) −12206.3 −1.65040
\(87\) 2021.54 + 2021.54i 0.267081 + 0.267081i
\(88\) 14347.2 14347.2i 1.85269 1.85269i
\(89\) 4763.09i 0.601324i −0.953731 0.300662i \(-0.902792\pi\)
0.953731 0.300662i \(-0.0972076\pi\)
\(90\) −22868.3 + 7481.47i −2.82325 + 0.923638i
\(91\) −929.153 −0.112203
\(92\) 7767.12 + 7767.12i 0.917666 + 0.917666i
\(93\) 9977.27 9977.27i 1.15357 1.15357i
\(94\) 15899.8i 1.79944i
\(95\) −4617.78 + 9108.34i −0.511666 + 1.00923i
\(96\) −17802.6 −1.93170
\(97\) 687.835 + 687.835i 0.0731039 + 0.0731039i 0.742713 0.669609i \(-0.233539\pi\)
−0.669609 + 0.742713i \(0.733539\pi\)
\(98\) −1758.85 + 1758.85i −0.183137 + 0.183137i
\(99\) 18034.9i 1.84011i
\(100\) −18446.5 + 13516.3i −1.84465 + 1.35163i
\(101\) −10449.3 −1.02434 −0.512172 0.858883i \(-0.671159\pi\)
−0.512172 + 0.858883i \(0.671159\pi\)
\(102\) 15506.7 + 15506.7i 1.49046 + 1.49046i
\(103\) 8531.35 8531.35i 0.804161 0.804161i −0.179582 0.983743i \(-0.557474\pi\)
0.983743 + 0.179582i \(0.0574744\pi\)
\(104\) 7490.90i 0.692576i
\(105\) −6037.16 3060.74i −0.547588 0.277619i
\(106\) 6617.16 0.588925
\(107\) −7239.61 7239.61i −0.632336 0.632336i 0.316318 0.948653i \(-0.397553\pi\)
−0.948653 + 0.316318i \(0.897553\pi\)
\(108\) 19560.9 19560.9i 1.67703 1.67703i
\(109\) 12097.6i 1.01823i −0.860699 0.509115i \(-0.829973\pi\)
0.860699 0.509115i \(-0.170027\pi\)
\(110\) 7660.41 + 23415.3i 0.633091 + 1.93515i
\(111\) 19128.0 1.55247
\(112\) −6513.27 6513.27i −0.519234 0.519234i
\(113\) −11639.0 + 11639.0i −0.911507 + 0.911507i −0.996391 0.0848839i \(-0.972948\pi\)
0.0848839 + 0.996391i \(0.472948\pi\)
\(114\) 43305.3i 3.33220i
\(115\) −7133.12 + 2333.63i −0.539367 + 0.176456i
\(116\) −7155.39 −0.531762
\(117\) 4708.15 + 4708.15i 0.343937 + 0.343937i
\(118\) −11770.6 + 11770.6i −0.845349 + 0.845349i
\(119\) 3831.01i 0.270533i
\(120\) 24675.9 48672.0i 1.71361 3.38000i
\(121\) 3825.30 0.261273
\(122\) 16403.3 + 16403.3i 1.10208 + 1.10208i
\(123\) −23767.4 + 23767.4i −1.57098 + 1.57098i
\(124\) 35315.3i 2.29678i
\(125\) −2537.75 15417.5i −0.162416 0.986722i
\(126\) 17824.7 1.12274
\(127\) 12421.7 + 12421.7i 0.770148 + 0.770148i 0.978132 0.207985i \(-0.0666904\pi\)
−0.207985 + 0.978132i \(0.566690\pi\)
\(128\) −9298.93 + 9298.93i −0.567562 + 0.567562i
\(129\) 24606.8i 1.47868i
\(130\) 8112.53 + 4112.92i 0.480031 + 0.243368i
\(131\) −12976.3 −0.756151 −0.378076 0.925775i \(-0.623414\pi\)
−0.378076 + 0.925775i \(0.623414\pi\)
\(132\) −51398.4 51398.4i −2.94986 2.94986i
\(133\) 5349.39 5349.39i 0.302414 0.302414i
\(134\) 62697.9i 3.49175i
\(135\) 5877.07 + 17964.2i 0.322473 + 0.985691i
\(136\) −30885.9 −1.66987
\(137\) −13425.8 13425.8i −0.715316 0.715316i 0.252326 0.967642i \(-0.418804\pi\)
−0.967642 + 0.252326i \(0.918804\pi\)
\(138\) 22504.7 22504.7i 1.18172 1.18172i
\(139\) 21541.5i 1.11493i 0.830201 + 0.557464i \(0.188225\pi\)
−0.830201 + 0.557464i \(0.811775\pi\)
\(140\) 16101.4 5267.63i 0.821499 0.268757i
\(141\) −32052.6 −1.61222
\(142\) 3796.64 + 3796.64i 0.188288 + 0.188288i
\(143\) 4820.76 4820.76i 0.235745 0.235745i
\(144\) 66007.3i 3.18322i
\(145\) 2210.74 4360.58i 0.105148 0.207400i
\(146\) 18082.9 0.848325
\(147\) 3545.67 + 3545.67i 0.164083 + 0.164083i
\(148\) −33852.6 + 33852.6i −1.54550 + 1.54550i
\(149\) 23088.6i 1.03998i −0.854173 0.519989i \(-0.825936\pi\)
0.854173 0.519989i \(-0.174064\pi\)
\(150\) 39162.6 + 53447.3i 1.74056 + 2.37544i
\(151\) 37589.4 1.64858 0.824292 0.566165i \(-0.191574\pi\)
0.824292 + 0.566165i \(0.191574\pi\)
\(152\) 43127.2 + 43127.2i 1.86665 + 1.86665i
\(153\) 19412.3 19412.3i 0.829265 0.829265i
\(154\) 18251.0i 0.769564i
\(155\) −21521.6 10911.1i −0.895799 0.454156i
\(156\) −26835.8 −1.10272
\(157\) −9237.11 9237.11i −0.374746 0.374746i 0.494457 0.869202i \(-0.335367\pi\)
−0.869202 + 0.494457i \(0.835367\pi\)
\(158\) −43120.6 + 43120.6i −1.72731 + 1.72731i
\(159\) 13339.6i 0.527651i
\(160\) 9466.21 + 28935.0i 0.369774 + 1.13027i
\(161\) 5559.89 0.214494
\(162\) −1551.84 1551.84i −0.0591311 0.0591311i
\(163\) 15066.0 15066.0i 0.567052 0.567052i −0.364249 0.931302i \(-0.618674\pi\)
0.931302 + 0.364249i \(0.118674\pi\)
\(164\) 84126.7i 3.12785i
\(165\) 47203.0 15442.6i 1.73381 0.567223i
\(166\) 60451.9 2.19378
\(167\) 10051.7 + 10051.7i 0.360416 + 0.360416i 0.863966 0.503550i \(-0.167973\pi\)
−0.503550 + 0.863966i \(0.667973\pi\)
\(168\) −28585.4 + 28585.4i −1.01281 + 1.01281i
\(169\) 26044.0i 0.911873i
\(170\) 16958.1 33449.0i 0.586785 1.15740i
\(171\) −54212.2 −1.85398
\(172\) −43548.8 43548.8i −1.47204 1.47204i
\(173\) −21678.9 + 21678.9i −0.724345 + 0.724345i −0.969487 0.245142i \(-0.921165\pi\)
0.245142 + 0.969487i \(0.421165\pi\)
\(174\) 20732.2i 0.684774i
\(175\) −1764.56 + 11439.9i −0.0576183 + 0.373547i
\(176\) 67586.0 2.18188
\(177\) 23728.5 + 23728.5i 0.757396 + 0.757396i
\(178\) 24424.3 24424.3i 0.770873 0.770873i
\(179\) 18170.8i 0.567111i 0.958956 + 0.283556i \(0.0915141\pi\)
−0.958956 + 0.283556i \(0.908486\pi\)
\(180\) −108280. 54896.1i −3.34197 1.69432i
\(181\) −43196.5 −1.31853 −0.659267 0.751909i \(-0.729133\pi\)
−0.659267 + 0.751909i \(0.729133\pi\)
\(182\) −4764.55 4764.55i −0.143840 0.143840i
\(183\) 33067.5 33067.5i 0.987415 0.987415i
\(184\) 44824.2i 1.32397i
\(185\) −10171.0 31089.3i −0.297180 0.908381i
\(186\) 102324. 2.95767
\(187\) −19876.6 19876.6i −0.568406 0.568406i
\(188\) 56726.3 56726.3i 1.60498 1.60498i
\(189\) 14002.2i 0.391987i
\(190\) −70385.3 + 23026.8i −1.94973 + 0.637863i
\(191\) 22892.9 0.627529 0.313764 0.949501i \(-0.398410\pi\)
0.313764 + 0.949501i \(0.398410\pi\)
\(192\) −9028.25 9028.25i −0.244907 0.244907i
\(193\) −37038.1 + 37038.1i −0.994338 + 0.994338i −0.999984 0.00564628i \(-0.998203\pi\)
0.00564628 + 0.999984i \(0.498203\pi\)
\(194\) 7054.21i 0.187433i
\(195\) 8291.26 16354.1i 0.218047 0.430087i
\(196\) −12550.2 −0.326691
\(197\) −2584.45 2584.45i −0.0665940 0.0665940i 0.673025 0.739619i \(-0.264994\pi\)
−0.739619 + 0.673025i \(0.764994\pi\)
\(198\) −92480.3 + 92480.3i −2.35895 + 2.35895i
\(199\) 21774.1i 0.549837i −0.961468 0.274919i \(-0.911349\pi\)
0.961468 0.274919i \(-0.0886509\pi\)
\(200\) −92229.0 14226.0i −2.30573 0.355650i
\(201\) −126393. −3.12846
\(202\) −53582.5 53582.5i −1.31317 1.31317i
\(203\) −2561.00 + 2561.00i −0.0621466 + 0.0621466i
\(204\) 110647.i 2.65877i
\(205\) 51267.8 + 25992.0i 1.21994 + 0.618488i
\(206\) 87494.7 2.06180
\(207\) −28172.8 28172.8i −0.657489 0.657489i
\(208\) 17643.8 17643.8i 0.407817 0.407817i
\(209\) 55508.9i 1.27078i
\(210\) −15262.6 46652.6i −0.346090 1.05788i
\(211\) 75363.5 1.69276 0.846382 0.532576i \(-0.178776\pi\)
0.846382 + 0.532576i \(0.178776\pi\)
\(212\) 23608.2 + 23608.2i 0.525280 + 0.525280i
\(213\) 7653.65 7653.65i 0.168698 0.168698i
\(214\) 74247.1i 1.62126i
\(215\) 39994.1 13084.2i 0.865205 0.283055i
\(216\) 112886. 2.41955
\(217\) 12639.8 + 12639.8i 0.268423 + 0.268423i
\(218\) 62034.4 62034.4i 1.30533 1.30533i
\(219\) 36453.4i 0.760063i
\(220\) −56209.1 + 110870.i −1.16135 + 2.29069i
\(221\) −10377.8 −0.212482
\(222\) 98085.4 + 98085.4i 1.99021 + 1.99021i
\(223\) −272.650 + 272.650i −0.00548271 + 0.00548271i −0.709843 0.704360i \(-0.751234\pi\)
0.704360 + 0.709843i \(0.251234\pi\)
\(224\) 22553.3i 0.449484i
\(225\) 66908.7 49026.2i 1.32165 0.968418i
\(226\) −119366. −2.33703
\(227\) −14283.0 14283.0i −0.277184 0.277184i 0.554800 0.831984i \(-0.312795\pi\)
−0.831984 + 0.554800i \(0.812795\pi\)
\(228\) 154501. 154501.i 2.97209 2.97209i
\(229\) 34740.0i 0.662458i 0.943550 + 0.331229i \(0.107463\pi\)
−0.943550 + 0.331229i \(0.892537\pi\)
\(230\) −48544.0 24611.0i −0.917655 0.465237i
\(231\) −36792.2 −0.689497
\(232\) −20647.0 20647.0i −0.383601 0.383601i
\(233\) −12274.1 + 12274.1i −0.226088 + 0.226088i −0.811056 0.584968i \(-0.801107\pi\)
0.584968 + 0.811056i \(0.301107\pi\)
\(234\) 48285.2i 0.881825i
\(235\) 17043.4 + 52096.0i 0.308618 + 0.943340i
\(236\) −83988.8 −1.50799
\(237\) 86927.0 + 86927.0i 1.54760 + 1.54760i
\(238\) −19644.8 + 19644.8i −0.346812 + 0.346812i
\(239\) 94956.1i 1.66237i 0.555997 + 0.831184i \(0.312336\pi\)
−0.555997 + 0.831184i \(0.687664\pi\)
\(240\) 172761. 56519.5i 2.99933 0.981242i
\(241\) 44563.2 0.767260 0.383630 0.923487i \(-0.374674\pi\)
0.383630 + 0.923487i \(0.374674\pi\)
\(242\) 19615.5 + 19615.5i 0.334942 + 0.334942i
\(243\) 40174.6 40174.6i 0.680361 0.680361i
\(244\) 117045.i 1.96596i
\(245\) 3877.53 7648.23i 0.0645986 0.127417i
\(246\) −243751. −4.02788
\(247\) 14491.0 + 14491.0i 0.237522 + 0.237522i
\(248\) −101903. + 101903.i −1.65685 + 1.65685i
\(249\) 121865.i 1.96554i
\(250\) 66045.5 92071.8i 1.05673 1.47315i
\(251\) −29296.1 −0.465010 −0.232505 0.972595i \(-0.574692\pi\)
−0.232505 + 0.972595i \(0.574692\pi\)
\(252\) 63593.5 + 63593.5i 1.00141 + 1.00141i
\(253\) −28846.6 + 28846.6i −0.450665 + 0.450665i
\(254\) 127393.i 1.97460i
\(255\) −67429.9 34185.9i −1.03698 0.525734i
\(256\) −109341. −1.66841
\(257\) −26697.7 26697.7i −0.404210 0.404210i 0.475504 0.879714i \(-0.342266\pi\)
−0.879714 + 0.475504i \(0.842266\pi\)
\(258\) −126180. + 126180.i −1.89561 + 1.89561i
\(259\) 24232.5i 0.361242i
\(260\) 14269.5 + 43617.0i 0.211087 + 0.645223i
\(261\) 25953.9 0.380997
\(262\) −66540.4 66540.4i −0.969355 0.969355i
\(263\) −69822.4 + 69822.4i −1.00945 + 1.00945i −0.00949086 + 0.999955i \(0.503021\pi\)
−0.999955 + 0.00949086i \(0.996979\pi\)
\(264\) 296621.i 4.25593i
\(265\) −21681.2 + 7093.08i −0.308739 + 0.101005i
\(266\) 54861.6 0.775364
\(267\) −49237.1 49237.1i −0.690669 0.690669i
\(268\) 223689. 223689.i 3.11440 3.11440i
\(269\) 73355.9i 1.01375i −0.862020 0.506875i \(-0.830801\pi\)
0.862020 0.506875i \(-0.169199\pi\)
\(270\) −61981.0 + 122254.i −0.850219 + 1.67701i
\(271\) 125134. 1.70388 0.851939 0.523642i \(-0.175427\pi\)
0.851939 + 0.523642i \(0.175427\pi\)
\(272\) −72747.6 72747.6i −0.983288 0.983288i
\(273\) −9604.87 + 9604.87i −0.128874 + 0.128874i
\(274\) 137690.i 1.83401i
\(275\) −50198.8 68509.0i −0.663785 0.905904i
\(276\) 160581. 2.10803
\(277\) 44216.3 + 44216.3i 0.576266 + 0.576266i 0.933872 0.357607i \(-0.116407\pi\)
−0.357607 + 0.933872i \(0.616407\pi\)
\(278\) −110461. + 110461.i −1.42929 + 1.42929i
\(279\) 128095.i 1.64560i
\(280\) 61660.5 + 31260.9i 0.786486 + 0.398736i
\(281\) 148338. 1.87862 0.939312 0.343065i \(-0.111465\pi\)
0.939312 + 0.343065i \(0.111465\pi\)
\(282\) −164360. 164360.i −2.06680 2.06680i
\(283\) −31339.4 + 31339.4i −0.391307 + 0.391307i −0.875153 0.483846i \(-0.839239\pi\)
0.483846 + 0.875153i \(0.339239\pi\)
\(284\) 27090.7i 0.335880i
\(285\) 46419.9 + 141890.i 0.571498 + 1.74688i
\(286\) 49440.1 0.604432
\(287\) −30110.0 30110.0i −0.365550 0.365550i
\(288\) −114281. + 114281.i −1.37781 + 1.37781i
\(289\) 40731.9i 0.487685i
\(290\) 33696.7 11024.0i 0.400674 0.131082i
\(291\) 14220.6 0.167932
\(292\) 64514.8 + 64514.8i 0.756648 + 0.756648i
\(293\) 65192.3 65192.3i 0.759383 0.759383i −0.216827 0.976210i \(-0.569571\pi\)
0.976210 + 0.216827i \(0.0695708\pi\)
\(294\) 36363.2i 0.420695i
\(295\) 25949.4 51183.8i 0.298183 0.588150i
\(296\) −195364. −2.22978
\(297\) 72647.9 + 72647.9i 0.823588 + 0.823588i
\(298\) 118394. 118394.i 1.33321 1.33321i
\(299\) 15061.2i 0.168468i
\(300\) −50964.1 + 330407.i −0.566268 + 3.67119i
\(301\) −31173.3 −0.344072
\(302\) 192752. + 192752.i 2.11342 + 2.11342i
\(303\) −108017. + 108017.i −1.17654 + 1.17654i
\(304\) 203161.i 2.19833i
\(305\) −71328.7 36162.5i −0.766769 0.388740i
\(306\) 199086. 2.12617
\(307\) −67430.3 67430.3i −0.715448 0.715448i 0.252221 0.967670i \(-0.418839\pi\)
−0.967670 + 0.252221i \(0.918839\pi\)
\(308\) 65114.5 65114.5i 0.686398 0.686398i
\(309\) 176381.i 1.84729i
\(310\) −54408.8 166310.i −0.566169 1.73059i
\(311\) 8860.75 0.0916114 0.0458057 0.998950i \(-0.485414\pi\)
0.0458057 + 0.998950i \(0.485414\pi\)
\(312\) −77435.1 77435.1i −0.795479 0.795479i
\(313\) −104602. + 104602.i −1.06771 + 1.06771i −0.0701733 + 0.997535i \(0.522355\pi\)
−0.997535 + 0.0701733i \(0.977645\pi\)
\(314\) 94732.7i 0.960817i
\(315\) −58402.6 + 19106.6i −0.588588 + 0.192559i
\(316\) −307685. −3.08129
\(317\) 40820.0 + 40820.0i 0.406213 + 0.406213i 0.880416 0.474203i \(-0.157264\pi\)
−0.474203 + 0.880416i \(0.657264\pi\)
\(318\) 68403.0 68403.0i 0.676427 0.676427i
\(319\) 26574.6i 0.261148i
\(320\) −9873.26 + 19474.5i −0.0964186 + 0.190181i
\(321\) −149675. −1.45258
\(322\) 28510.2 + 28510.2i 0.274972 + 0.274972i
\(323\) 59748.1 59748.1i 0.572689 0.572689i
\(324\) 11073.1i 0.105482i
\(325\) −30989.5 4780.02i −0.293392 0.0452546i
\(326\) 154512. 1.45388
\(327\) −125055. 125055.i −1.16952 1.16952i
\(328\) 242749. 242749.i 2.25636 2.25636i
\(329\) 40606.1i 0.375145i
\(330\) 321237. + 162862.i 2.94983 + 1.49552i
\(331\) −14561.0 −0.132903 −0.0664514 0.997790i \(-0.521168\pi\)
−0.0664514 + 0.997790i \(0.521168\pi\)
\(332\) 215676. + 215676.i 1.95671 + 1.95671i
\(333\) 122789. 122789.i 1.10732 1.10732i
\(334\) 103087.i 0.924079i
\(335\) 67207.2 + 205430.i 0.598862 + 1.83052i
\(336\) −134658. −1.19276
\(337\) −52044.1 52044.1i −0.458259 0.458259i 0.439824 0.898084i \(-0.355041\pi\)
−0.898084 + 0.439824i \(0.855041\pi\)
\(338\) −133549. + 133549.i −1.16898 + 1.16898i
\(339\) 240631.i 2.09388i
\(340\) 179838. 58834.9i 1.55570 0.508952i
\(341\) −131159. −1.12795
\(342\) −277992. 277992.i −2.37673 2.37673i
\(343\) −4491.86 + 4491.86i −0.0381802 + 0.0381802i
\(344\) 251321.i 2.12379i
\(345\) −49613.5 + 97860.0i −0.416832 + 0.822180i
\(346\) −222332. −1.85716
\(347\) 17334.3 + 17334.3i 0.143962 + 0.143962i 0.775414 0.631453i \(-0.217541\pi\)
−0.631453 + 0.775414i \(0.717541\pi\)
\(348\) −73966.8 + 73966.8i −0.610771 + 0.610771i
\(349\) 125838.i 1.03314i 0.856244 + 0.516572i \(0.172792\pi\)
−0.856244 + 0.516572i \(0.827208\pi\)
\(350\) −67710.2 + 49613.4i −0.552736 + 0.405008i
\(351\) 37930.5 0.307875
\(352\) 117014. + 117014.i 0.944394 + 0.944394i
\(353\) 58739.2 58739.2i 0.471388 0.471388i −0.430976 0.902364i \(-0.641830\pi\)
0.902364 + 0.430976i \(0.141830\pi\)
\(354\) 243351.i 1.94190i
\(355\) −16509.4 8370.01i −0.131001 0.0664155i
\(356\) 174279. 1.37513
\(357\) 39602.0 + 39602.0i 0.310729 + 0.310729i
\(358\) −93177.0 + 93177.0i −0.727014 + 0.727014i
\(359\) 131534.i 1.02059i 0.860000 + 0.510294i \(0.170463\pi\)
−0.860000 + 0.510294i \(0.829537\pi\)
\(360\) −154039. 470846.i −1.18857 3.63307i
\(361\) −36536.2 −0.280355
\(362\) −221505. 221505.i −1.69031 1.69031i
\(363\) 39543.0 39543.0i 0.300094 0.300094i
\(364\) 33997.2i 0.256590i
\(365\) −59248.7 + 19383.5i −0.444727 + 0.145494i
\(366\) 339130. 2.53165
\(367\) 13662.1 + 13662.1i 0.101434 + 0.101434i 0.756003 0.654568i \(-0.227150\pi\)
−0.654568 + 0.756003i \(0.727150\pi\)
\(368\) −105577. + 105577.i −0.779607 + 0.779607i
\(369\) 305143.i 2.24104i
\(370\) 107266. 211576.i 0.783534 1.54548i
\(371\) 16899.3 0.122778
\(372\) 365062. + 365062.i 2.63804 + 2.63804i
\(373\) 155910. 155910.i 1.12061 1.12061i 0.128964 0.991649i \(-0.458835\pi\)
0.991649 0.128964i \(-0.0411652\pi\)
\(374\) 203848.i 1.45735i
\(375\) −185608. 133141.i −1.31988 0.946783i
\(376\) 327369. 2.31559
\(377\) −6937.49 6937.49i −0.0488112 0.0488112i
\(378\) 71800.8 71800.8i 0.502511 0.502511i
\(379\) 74194.8i 0.516530i 0.966074 + 0.258265i \(0.0831507\pi\)
−0.966074 + 0.258265i \(0.916849\pi\)
\(380\) −333269. 168962.i −2.30796 1.17010i
\(381\) 256812. 1.76915
\(382\) 117391. + 117391.i 0.804467 + 0.804467i
\(383\) 153589. 153589.i 1.04704 1.04704i 0.0482041 0.998838i \(-0.484650\pi\)
0.998838 0.0482041i \(-0.0153498\pi\)
\(384\) 192250.i 1.30378i
\(385\) 19563.6 + 59799.5i 0.131986 + 0.403437i
\(386\) −379851. −2.54940
\(387\) 157959. + 157959.i 1.05469 + 1.05469i
\(388\) −25167.5 + 25167.5i −0.167177 + 0.167177i
\(389\) 5566.71i 0.0367874i 0.999831 + 0.0183937i \(0.00585523\pi\)
−0.999831 + 0.0183937i \(0.994145\pi\)
\(390\) 126377. 41344.8i 0.830883 0.271827i
\(391\) 62099.2 0.406193
\(392\) −36213.7 36213.7i −0.235668 0.235668i
\(393\) −134139. + 134139.i −0.868501 + 0.868501i
\(394\) 26505.2i 0.170742i
\(395\) 95063.0 187507.i 0.609281 1.20177i
\(396\) −659888. −4.20804
\(397\) −88916.2 88916.2i −0.564157 0.564157i 0.366329 0.930486i \(-0.380615\pi\)
−0.930486 + 0.366329i \(0.880615\pi\)
\(398\) 111654. 111654.i 0.704869 0.704869i
\(399\) 110596.i 0.694693i
\(400\) −183726. 250741.i −1.14829 1.56713i
\(401\) 140901. 0.876242 0.438121 0.898916i \(-0.355644\pi\)
0.438121 + 0.898916i \(0.355644\pi\)
\(402\) −648122. 648122.i −4.01056 4.01056i
\(403\) −34239.9 + 34239.9i −0.210825 + 0.210825i
\(404\) 382335.i 2.34251i
\(405\) 6748.05 + 3421.16i 0.0411404 + 0.0208575i
\(406\) −26264.8 −0.159339
\(407\) −125726. 125726.i −0.758992 0.758992i
\(408\) −319274. + 319274.i −1.91798 + 1.91798i
\(409\) 36303.3i 0.217020i −0.994095 0.108510i \(-0.965392\pi\)
0.994095 0.108510i \(-0.0346079\pi\)
\(410\) 129610. + 396176.i 0.771032 + 2.35679i
\(411\) −277570. −1.64320
\(412\) 312157. + 312157.i 1.83899 + 1.83899i
\(413\) −30060.6 + 30060.6i −0.176237 + 0.176237i
\(414\) 288931.i 1.68575i
\(415\) −198071. + 64799.8i −1.15007 + 0.376251i
\(416\) 61094.8 0.353035
\(417\) 222679. + 222679.i 1.28058 + 1.28058i
\(418\) −284641. + 284641.i −1.62909 + 1.62909i
\(419\) 135974.i 0.774510i −0.921973 0.387255i \(-0.873423\pi\)
0.921973 0.387255i \(-0.126577\pi\)
\(420\) 111991. 220896.i 0.634869 1.25225i
\(421\) −48464.2 −0.273437 −0.136718 0.990610i \(-0.543656\pi\)
−0.136718 + 0.990610i \(0.543656\pi\)
\(422\) 386452. + 386452.i 2.17005 + 2.17005i
\(423\) −205757. + 205757.i −1.14993 + 1.14993i
\(424\) 136243.i 0.757851i
\(425\) −19708.6 + 127773.i −0.109113 + 0.707396i
\(426\) 78493.4 0.432528
\(427\) 41891.9 + 41891.9i 0.229760 + 0.229760i
\(428\) 264893. 264893.i 1.44605 1.44605i
\(429\) 99666.5i 0.541545i
\(430\) 272177. + 137990.i 1.47202 + 0.746293i
\(431\) 103330. 0.556251 0.278126 0.960545i \(-0.410287\pi\)
0.278126 + 0.960545i \(0.410287\pi\)
\(432\) 265889. + 265889.i 1.42473 + 1.42473i
\(433\) −166967. + 166967.i −0.890541 + 0.890541i −0.994574 0.104033i \(-0.966825\pi\)
0.104033 + 0.994574i \(0.466825\pi\)
\(434\) 129629.i 0.688215i
\(435\) −22223.3 67929.2i −0.117444 0.358987i
\(436\) 442644. 2.32853
\(437\) −86711.5 86711.5i −0.454061 0.454061i
\(438\) 186927. 186927.i 0.974370 0.974370i
\(439\) 153188.i 0.794870i −0.917630 0.397435i \(-0.869900\pi\)
0.917630 0.397435i \(-0.130100\pi\)
\(440\) −482108. + 157723.i −2.49022 + 0.814687i
\(441\) 45521.8 0.234068
\(442\) −53215.9 53215.9i −0.272393 0.272393i
\(443\) 193497. 193497.i 0.985977 0.985977i −0.0139263 0.999903i \(-0.504433\pi\)
0.999903 + 0.0139263i \(0.00443303\pi\)
\(444\) 699883.i 3.55026i
\(445\) −53845.5 + 106208.i −0.271913 + 0.536334i
\(446\) −2796.21 −0.0140572
\(447\) −238672. 238672.i −1.19450 1.19450i
\(448\) 11437.5 11437.5i 0.0569870 0.0569870i
\(449\) 197644.i 0.980371i 0.871618 + 0.490185i \(0.163071\pi\)
−0.871618 + 0.490185i \(0.836929\pi\)
\(450\) 594495. + 91698.8i 2.93578 + 0.452834i
\(451\) 312441. 1.53608
\(452\) −425866. 425866.i −2.08447 2.08447i
\(453\) 388570. 388570.i 1.89353 1.89353i
\(454\) 146482.i 0.710677i
\(455\) 20718.3 + 10503.8i 0.100076 + 0.0507371i
\(456\) 891631. 4.28801
\(457\) −112416. 112416.i −0.538264 0.538264i 0.384755 0.923019i \(-0.374286\pi\)
−0.923019 + 0.384755i \(0.874286\pi\)
\(458\) −178141. + 178141.i −0.849244 + 0.849244i
\(459\) 156392.i 0.742317i
\(460\) −85386.2 260997.i −0.403526 1.23344i
\(461\) 99283.0 0.467168 0.233584 0.972337i \(-0.424955\pi\)
0.233584 + 0.972337i \(0.424955\pi\)
\(462\) −188665. 188665.i −0.883907 0.883907i
\(463\) −102537. + 102537.i −0.478319 + 0.478319i −0.904594 0.426275i \(-0.859826\pi\)
0.426275 + 0.904594i \(0.359826\pi\)
\(464\) 97262.2i 0.451761i
\(465\) −335264. + 109683.i −1.55053 + 0.507263i
\(466\) −125879. −0.579671
\(467\) 265905. + 265905.i 1.21925 + 1.21925i 0.967895 + 0.251353i \(0.0808755\pi\)
0.251353 + 0.967895i \(0.419124\pi\)
\(468\) −172268. + 172268.i −0.786528 + 0.786528i
\(469\) 160122.i 0.727956i
\(470\) −179744. + 354535.i −0.813689 + 1.60496i
\(471\) −190972. −0.860851
\(472\) −242351. 242351.i −1.08783 1.08783i
\(473\) 161738. 161738.i 0.722917 0.722917i
\(474\) 891495.i 3.96791i
\(475\) 205935. 150895.i 0.912731 0.668788i
\(476\) −140175. −0.618665
\(477\) −85631.2 85631.2i −0.376353 0.376353i
\(478\) −486920. + 486920.i −2.13109 + 2.13109i
\(479\) 246167.i 1.07290i −0.843932 0.536449i \(-0.819765\pi\)
0.843932 0.536449i \(-0.180235\pi\)
\(480\) 396962. + 201254.i 1.72293 + 0.873497i
\(481\) −65643.4 −0.283727
\(482\) 228513. + 228513.i 0.983596 + 0.983596i
\(483\) 57473.9 57473.9i 0.246363 0.246363i
\(484\) 139966.i 0.597490i
\(485\) −7561.57 23113.2i −0.0321461 0.0982598i
\(486\) 412018. 1.74439
\(487\) −47449.1 47449.1i −0.200065 0.200065i 0.599963 0.800028i \(-0.295182\pi\)
−0.800028 + 0.599963i \(0.795182\pi\)
\(488\) −337735. + 337735.i −1.41820 + 1.41820i
\(489\) 311482.i 1.30261i
\(490\) 59102.2 19335.5i 0.246157 0.0805311i
\(491\) 138021. 0.572508 0.286254 0.958154i \(-0.407590\pi\)
0.286254 + 0.958154i \(0.407590\pi\)
\(492\) −869637. 869637.i −3.59259 3.59259i
\(493\) −28604.1 + 28604.1i −0.117689 + 0.117689i
\(494\) 148615.i 0.608987i
\(495\) 203881. 402144.i 0.832081 1.64124i
\(496\) −480037. −1.95124
\(497\) 9696.09 + 9696.09i 0.0392540 + 0.0392540i
\(498\) 624905. 624905.i 2.51974 2.51974i
\(499\) 450282.i 1.80835i −0.427158 0.904177i \(-0.640485\pi\)
0.427158 0.904177i \(-0.359515\pi\)
\(500\) 564119. 92854.7i 2.25648 0.371419i
\(501\) 207812. 0.827935
\(502\) −150226. 150226.i −0.596124 0.596124i
\(503\) −269041. + 269041.i −1.06337 + 1.06337i −0.0655153 + 0.997852i \(0.520869\pi\)
−0.997852 + 0.0655153i \(0.979131\pi\)
\(504\) 367000.i 1.44479i
\(505\) 233000. + 118127.i 0.913635 + 0.463198i
\(506\) −295841. −1.15547
\(507\) 269223. + 269223.i 1.04736 + 1.04736i
\(508\) −454503. + 454503.i −1.76120 + 1.76120i
\(509\) 91831.8i 0.354452i 0.984170 + 0.177226i \(0.0567123\pi\)
−0.984170 + 0.177226i \(0.943288\pi\)
\(510\) −170470. 521069.i −0.655401 2.00334i
\(511\) 46181.3 0.176858
\(512\) −411899. 411899.i −1.57127 1.57127i
\(513\) −218376. + 218376.i −0.829795 + 0.829795i
\(514\) 273803.i 1.03636i
\(515\) −286677. + 93787.6i −1.08088 + 0.353615i
\(516\) −900348. −3.38151
\(517\) 210678. + 210678.i 0.788202 + 0.788202i
\(518\) −124260. + 124260.i −0.463098 + 0.463098i
\(519\) 448200.i 1.66394i
\(520\) −84682.7 + 167032.i −0.313176 + 0.617723i
\(521\) −317145. −1.16838 −0.584189 0.811618i \(-0.698587\pi\)
−0.584189 + 0.811618i \(0.698587\pi\)
\(522\) 133087. + 133087.i 0.488422 + 0.488422i
\(523\) 201425. 201425.i 0.736394 0.736394i −0.235484 0.971878i \(-0.575668\pi\)
0.971878 + 0.235484i \(0.0756676\pi\)
\(524\) 474796.i 1.72920i
\(525\) 100016. + 136497.i 0.362869 + 0.495228i
\(526\) −716075. −2.58814
\(527\) 141175. + 141175.i 0.508321 + 0.508321i
\(528\) 698652. 698652.i 2.50607 2.50607i
\(529\) 189717.i 0.677947i
\(530\) −147550. 74805.3i −0.525275 0.266306i
\(531\) 304642. 1.08044
\(532\) 195731. + 195731.i 0.691571 + 0.691571i
\(533\) 81564.9 81564.9i 0.287110 0.287110i
\(534\) 504960.i 1.77082i
\(535\) 79587.1 + 243271.i 0.278058 + 0.849930i
\(536\) 1.29091e6 4.49332
\(537\) 187836. + 187836.i 0.651373 + 0.651373i
\(538\) 376157. 376157.i 1.29959 1.29959i
\(539\) 46610.5i 0.160438i
\(540\) −657301. + 215039.i −2.25412 + 0.737443i
\(541\) −288032. −0.984115 −0.492058 0.870563i \(-0.663755\pi\)
−0.492058 + 0.870563i \(0.663755\pi\)
\(542\) 641669. + 641669.i 2.18430 + 2.18430i
\(543\) −446532. + 446532.i −1.51444 + 1.51444i
\(544\) 251901.i 0.851202i
\(545\) −136760. + 269752.i −0.460433 + 0.908181i
\(546\) −98504.4 −0.330423
\(547\) 84502.3 + 84502.3i 0.282419 + 0.282419i 0.834073 0.551654i \(-0.186003\pi\)
−0.551654 + 0.834073i \(0.686003\pi\)
\(548\) 491241. 491241.i 1.63581 1.63581i
\(549\) 424544.i 1.40857i
\(550\) 93892.0 608714.i 0.310387 2.01228i
\(551\) 79882.2 0.263116
\(552\) 463358. + 463358.i 1.52068 + 1.52068i
\(553\) −110124. + 110124.i −0.360108 + 0.360108i
\(554\) 453468.i 1.47750i
\(555\) −426517. 216237.i −1.38468 0.702013i
\(556\) −788192. −2.54966
\(557\) −83519.3 83519.3i −0.269201 0.269201i 0.559577 0.828778i \(-0.310964\pi\)
−0.828778 + 0.559577i \(0.810964\pi\)
\(558\) 656851. 656851.i 2.10959 2.10959i
\(559\) 84445.4i 0.270242i
\(560\) 71602.2 + 218864.i 0.228323 + 0.697908i
\(561\) −410937. −1.30572
\(562\) 760653. + 760653.i 2.40832 + 2.40832i
\(563\) −377217. + 377217.i −1.19008 + 1.19008i −0.213030 + 0.977046i \(0.568333\pi\)
−0.977046 + 0.213030i \(0.931667\pi\)
\(564\) 1.17279e6i 3.68689i
\(565\) 391104. 127951.i 1.22517 0.400818i
\(566\) −321406. −1.00328
\(567\) −3963.18 3963.18i −0.0123276 0.0123276i
\(568\) −78170.6 + 78170.6i −0.242296 + 0.242296i
\(569\) 4157.76i 0.0128421i 0.999979 + 0.00642103i \(0.00204389\pi\)
−0.999979 + 0.00642103i \(0.997956\pi\)
\(570\) −489555. + 965623.i −1.50679 + 2.97206i
\(571\) 281259. 0.862650 0.431325 0.902197i \(-0.358046\pi\)
0.431325 + 0.902197i \(0.358046\pi\)
\(572\) 176389. + 176389.i 0.539112 + 0.539112i
\(573\) 236649. 236649.i 0.720768 0.720768i
\(574\) 308798.i 0.937240i
\(575\) 185436. + 28602.8i 0.560864 + 0.0865114i
\(576\) −115911. −0.349365
\(577\) −363376. 363376.i −1.09145 1.09145i −0.995374 0.0960790i \(-0.969370\pi\)
−0.0960790 0.995374i \(-0.530630\pi\)
\(578\) 208867. 208867.i 0.625192 0.625192i
\(579\) 765742.i 2.28415i
\(580\) 159551. + 80889.9i 0.474290 + 0.240457i
\(581\) 154386. 0.457357
\(582\) 72921.0 + 72921.0i 0.215281 + 0.215281i
\(583\) −87679.3 + 87679.3i −0.257965 + 0.257965i
\(584\) 372317.i 1.09166i
\(585\) −51758.0 158207.i −0.151240 0.462289i
\(586\) 668591. 1.94700
\(587\) −90438.2 90438.2i −0.262467 0.262467i 0.563588 0.826056i \(-0.309420\pi\)
−0.826056 + 0.563588i \(0.809420\pi\)
\(588\) −129734. + 129734.i −0.375231 + 0.375231i
\(589\) 394258.i 1.13645i
\(590\) 395526. 129398.i 1.13624 0.371726i
\(591\) −53432.0 −0.152977
\(592\) −460154. 460154.i −1.31298 1.31298i
\(593\) 54345.8 54345.8i 0.154546 0.154546i −0.625599 0.780145i \(-0.715145\pi\)
0.780145 + 0.625599i \(0.215145\pi\)
\(594\) 745053.i 2.11161i
\(595\) 43308.7 85424.1i 0.122332 0.241294i
\(596\) 844798. 2.37826
\(597\) −225084. 225084.i −0.631532 0.631532i
\(598\) −77231.4 + 77231.4i −0.215969 + 0.215969i
\(599\) 49282.3i 0.137353i −0.997639 0.0686764i \(-0.978122\pi\)
0.997639 0.0686764i \(-0.0218776\pi\)
\(600\) −1.10045e6 + 806335.i −3.05681 + 2.23982i
\(601\) −520219. −1.44025 −0.720123 0.693846i \(-0.755915\pi\)
−0.720123 + 0.693846i \(0.755915\pi\)
\(602\) −159852. 159852.i −0.441087 0.441087i
\(603\) −811360. + 811360.i −2.23141 + 2.23141i
\(604\) 1.37537e6i 3.77005i
\(605\) −85296.8 43244.1i −0.233035 0.118145i
\(606\) −1.10779e6 −3.01656
\(607\) 151266. + 151266.i 0.410547 + 0.410547i 0.881929 0.471382i \(-0.156245\pi\)
−0.471382 + 0.881929i \(0.656245\pi\)
\(608\) −351740. + 351740.i −0.951511 + 0.951511i
\(609\) 52947.3i 0.142761i
\(610\) −180326. 551198.i −0.484618 1.48132i
\(611\) 109998. 0.294647
\(612\) 710284. + 710284.i 1.89640 + 1.89640i
\(613\) 55744.1 55744.1i 0.148347 0.148347i −0.629032 0.777379i \(-0.716549\pi\)
0.777379 + 0.629032i \(0.216549\pi\)
\(614\) 691543.i 1.83435i
\(615\) 798652. 261282.i 2.11158 0.690812i
\(616\) 375777. 0.990306
\(617\) −298648. 298648.i −0.784493 0.784493i 0.196093 0.980585i \(-0.437175\pi\)
−0.980585 + 0.196093i \(0.937175\pi\)
\(618\) 904453. 904453.i 2.36815 2.36815i
\(619\) 345096.i 0.900656i 0.892863 + 0.450328i \(0.148693\pi\)
−0.892863 + 0.450328i \(0.851307\pi\)
\(620\) 399231. 787462.i 1.03858 2.04855i
\(621\) −226969. −0.588551
\(622\) 45436.5 + 45436.5i 0.117442 + 0.117442i
\(623\) 62376.5 62376.5i 0.160711 0.160711i
\(624\) 364776.i 0.936822i
\(625\) −117705. + 372469.i −0.301324 + 0.953522i
\(626\) −1.07277e6 −2.73752
\(627\) 573808. + 573808.i 1.45959 + 1.45959i
\(628\) 337980. 337980.i 0.856983 0.856983i
\(629\) 270656.i 0.684095i
\(630\) −397455. 201503.i −1.00140 0.507693i
\(631\) −184294. −0.462864 −0.231432 0.972851i \(-0.574341\pi\)
−0.231432 + 0.972851i \(0.574341\pi\)
\(632\) −887829. 887829.i −2.22277 2.22277i
\(633\) 779050. 779050.i 1.94428 1.94428i
\(634\) 418636.i 1.04150i
\(635\) −136555. 417404.i −0.338658 1.03516i
\(636\) 488087. 1.20665
\(637\) −12168.0 12168.0i −0.0299875 0.0299875i
\(638\) 136270. 136270.i 0.334781 0.334781i
\(639\) 98262.9i 0.240651i
\(640\) 312470. 102226.i 0.762866 0.249575i
\(641\) −538716. −1.31112 −0.655562 0.755142i \(-0.727568\pi\)
−0.655562 + 0.755142i \(0.727568\pi\)
\(642\) −767509. 767509.i −1.86214 1.86214i
\(643\) −95071.3 + 95071.3i −0.229947 + 0.229947i −0.812670 0.582724i \(-0.801987\pi\)
0.582724 + 0.812670i \(0.301987\pi\)
\(644\) 203433.i 0.490513i
\(645\) 278174. 548683.i 0.668646 1.31887i
\(646\) 612757. 1.46833
\(647\) 90118.2 + 90118.2i 0.215280 + 0.215280i 0.806506 0.591226i \(-0.201356\pi\)
−0.591226 + 0.806506i \(0.701356\pi\)
\(648\) 31951.4 31951.4i 0.0760922 0.0760922i
\(649\) 311929.i 0.740570i
\(650\) −134398. 183420.i −0.318102 0.434131i
\(651\) 261321. 0.616611
\(652\) 551257. + 551257.i 1.29676 + 1.29676i
\(653\) −242315. + 242315.i −0.568268 + 0.568268i −0.931643 0.363375i \(-0.881624\pi\)
0.363375 + 0.931643i \(0.381624\pi\)
\(654\) 1.28253e6i 2.99855i
\(655\) 289346. + 146694.i 0.674428 + 0.341924i
\(656\) 1.14352e6 2.65728
\(657\) −234007. 234007.i −0.542123 0.542123i
\(658\) 208221. 208221.i 0.480921 0.480921i
\(659\) 682462.i 1.57148i 0.618559 + 0.785738i \(0.287717\pi\)
−0.618559 + 0.785738i \(0.712283\pi\)
\(660\) 565037. + 1.72713e6i 1.29715 + 3.96494i
\(661\) 125400. 0.287008 0.143504 0.989650i \(-0.454163\pi\)
0.143504 + 0.989650i \(0.454163\pi\)
\(662\) −74666.2 74666.2i −0.170376 0.170376i
\(663\) −107278. + 107278.i −0.244053 + 0.244053i
\(664\) 1.24467e6i 2.82305i
\(665\) −179755. + 58807.4i −0.406478 + 0.132981i
\(666\) 1.25929e6 2.83907
\(667\) 41512.8 + 41512.8i 0.0933104 + 0.0933104i
\(668\) −367784. + 367784.i −0.824215 + 0.824215i
\(669\) 5636.88i 0.0125947i
\(670\) −708784. + 1.39804e6i −1.57893 + 3.11437i
\(671\) −434698. −0.965479
\(672\) −233139. 233139.i −0.516269 0.516269i
\(673\) 103115. 103115.i 0.227662 0.227662i −0.584053 0.811715i \(-0.698534\pi\)
0.811715 + 0.584053i \(0.198534\pi\)
\(674\) 533747.i 1.17494i
\(675\) 72034.0 467006.i 0.158099 1.02498i
\(676\) −952936. −2.08531
\(677\) −620376. 620376.i −1.35356 1.35356i −0.881643 0.471917i \(-0.843562\pi\)
−0.471917 0.881643i \(-0.656438\pi\)
\(678\) −1.23391e6 + 1.23391e6i −2.68427 + 2.68427i
\(679\) 18015.5i 0.0390757i
\(680\) 688695. + 349157.i 1.48939 + 0.755098i
\(681\) −295294. −0.636736
\(682\) −672561. 672561.i −1.44598 1.44598i
\(683\) 484076. 484076.i 1.03770 1.03770i 0.0384396 0.999261i \(-0.487761\pi\)
0.999261 0.0384396i \(-0.0122387\pi\)
\(684\) 1.98359e6i 4.23976i
\(685\) 147593. + 451143.i 0.314547 + 0.961465i
\(686\) −46067.1 −0.0978909
\(687\) 359115. + 359115.i 0.760886 + 0.760886i
\(688\) 591954. 591954.i 1.25058 1.25058i
\(689\) 45778.6i 0.0964326i
\(690\) −756220. + 247400.i −1.58836 + 0.519639i
\(691\) −813004. −1.70269 −0.851347 0.524603i \(-0.824214\pi\)
−0.851347 + 0.524603i \(0.824214\pi\)
\(692\) −793219. 793219.i −1.65646 1.65646i
\(693\) −236182. + 236182.i −0.491791 + 0.491791i
\(694\) 177775.i 0.369106i
\(695\) 243521. 480334.i 0.504159 0.994428i
\(696\) −426864. −0.881194
\(697\) −336302. 336302.i −0.692252 0.692252i
\(698\) −645277. + 645277.i −1.32445 + 1.32445i
\(699\) 253760.i 0.519360i
\(700\) −418578. 64564.3i −0.854242 0.131764i
\(701\) 409417. 0.833163 0.416581 0.909098i \(-0.363228\pi\)
0.416581 + 0.909098i \(0.363228\pi\)
\(702\) 194501. + 194501.i 0.394683 + 0.394683i
\(703\) 377927. 377927.i 0.764712 0.764712i
\(704\) 118683.i 0.239466i
\(705\) 714709. + 362346.i 1.43797 + 0.729030i
\(706\) 602410. 1.20860
\(707\) −136842. 136842.i −0.273768 0.273768i
\(708\) −868211. + 868211.i −1.73204 + 1.73204i
\(709\) 147502.i 0.293430i −0.989179 0.146715i \(-0.953130\pi\)
0.989179 0.146715i \(-0.0468701\pi\)
\(710\) −41737.5 127578.i −0.0827961 0.253080i
\(711\) 1.11603e6 2.20768
\(712\) 502883. + 502883.i 0.991990 + 0.991990i
\(713\) 204886. 204886.i 0.403026 0.403026i
\(714\) 406146.i 0.796683i
\(715\) −161991. + 52996.0i −0.316868 + 0.103665i
\(716\) −664860. −1.29689
\(717\) 981583. + 981583.i 1.90936 + 1.90936i
\(718\) −674487. + 674487.i −1.30835 + 1.30835i
\(719\) 60901.4i 0.117807i 0.998264 + 0.0589033i \(0.0187604\pi\)
−0.998264 + 0.0589033i \(0.981240\pi\)
\(720\) 746196. 1.47183e6i 1.43942 2.83918i
\(721\) 223450. 0.429842
\(722\) −187352. 187352.i −0.359404 0.359404i
\(723\) 460660. 460660.i 0.881260 0.881260i
\(724\) 1.58054e6i 3.01528i
\(725\) −98590.5 + 72240.4i −0.187568 + 0.137437i
\(726\) 405541. 0.769416
\(727\) −401016. 401016.i −0.758739 0.758739i 0.217354 0.976093i \(-0.430257\pi\)
−0.976093 + 0.217354i \(0.930257\pi\)
\(728\) 98099.3 98099.3i 0.185099 0.185099i
\(729\) 855102.i 1.60903i
\(730\) −403213. 204423.i −0.756639 0.383604i
\(731\) −348179. −0.651580
\(732\) 1.20992e6 + 1.20992e6i 2.25806 + 2.25806i
\(733\) −171074. + 171074.i −0.318403 + 0.318403i −0.848153 0.529751i \(-0.822285\pi\)
0.529751 + 0.848153i \(0.322285\pi\)
\(734\) 140114.i 0.260070i
\(735\) −38978.6 119144.i −0.0721524 0.220546i
\(736\) −365581. −0.674881
\(737\) 830766. + 830766.i 1.52948 + 1.52948i
\(738\) −1.56472e6 + 1.56472e6i −2.87293 + 2.87293i
\(739\) 698841.i 1.27965i −0.768522 0.639823i \(-0.779008\pi\)
0.768522 0.639823i \(-0.220992\pi\)
\(740\) 1.13754e6 372151.i 2.07732 0.679604i
\(741\) 299593. 0.545626
\(742\) 86657.0 + 86657.0i 0.157397 + 0.157397i
\(743\) −163993. + 163993.i −0.297062 + 0.297062i −0.839862 0.542800i \(-0.817364\pi\)
0.542800 + 0.839862i \(0.317364\pi\)
\(744\) 2.10678e6i 3.80605i
\(745\) −261011. + 514830.i −0.470268 + 0.927580i
\(746\) 1.59896e6 2.87316
\(747\) −782295. 782295.i −1.40194 1.40194i
\(748\) 727273. 727273.i 1.29985 1.29985i
\(749\) 189617.i 0.337998i
\(750\) −269040. 1.63449e6i −0.478293 2.90577i
\(751\) 648908. 1.15054 0.575272 0.817962i \(-0.304896\pi\)
0.575272 + 0.817962i \(0.304896\pi\)
\(752\) 771073. + 771073.i 1.36352 + 1.36352i
\(753\) −302840. + 302840.i −0.534101 + 0.534101i
\(754\) 71148.7i 0.125148i
\(755\) −838169. 424938.i −1.47041 0.745473i
\(756\) 512331. 0.896411
\(757\) −427480. 427480.i −0.745975 0.745975i 0.227746 0.973721i \(-0.426865\pi\)
−0.973721 + 0.227746i \(0.926865\pi\)
\(758\) −380459. + 380459.i −0.662170 + 0.662170i
\(759\) 596387.i 1.03525i
\(760\) −474109. 1.44919e6i −0.820827 2.50899i
\(761\) 277901. 0.479867 0.239934 0.970789i \(-0.422874\pi\)
0.239934 + 0.970789i \(0.422874\pi\)
\(762\) 1.31689e6 + 1.31689e6i 2.26798 + 2.26798i
\(763\) 158428. 158428.i 0.272133 0.272133i
\(764\) 837638.i 1.43506i
\(765\) −652307. + 213405.i −1.11463 + 0.364654i
\(766\) 1.57516e6 2.68453
\(767\) −81431.2 81431.2i −0.138420 0.138420i
\(768\) −1.13028e6 + 1.13028e6i −1.91630 + 1.91630i
\(769\) 347634.i 0.587855i −0.955828 0.293927i \(-0.905038\pi\)
0.955828 0.293927i \(-0.0949624\pi\)
\(770\) −206323. + 406961.i −0.347989 + 0.686391i
\(771\) −551960. −0.928536
\(772\) −1.35520e6 1.35520e6i −2.27389 2.27389i
\(773\) 264187. 264187.i 0.442132 0.442132i −0.450596 0.892728i \(-0.648788\pi\)
0.892728 + 0.450596i \(0.148788\pi\)
\(774\) 1.61998e6i 2.70413i
\(775\) 356542. + 486592.i 0.593618 + 0.810143i
\(776\) −145242. −0.241196
\(777\) 250497. + 250497.i 0.414916 + 0.414916i
\(778\) −28545.2 + 28545.2i −0.0471600 + 0.0471600i
\(779\) 939184.i 1.54766i
\(780\) 598386. + 303372.i 0.983541 + 0.498640i
\(781\) −100613. −0.164950
\(782\) 318435. + 318435.i 0.520723 + 0.520723i
\(783\) 104547. 104547.i 0.170525 0.170525i
\(784\) 170593.i 0.277542i
\(785\) 101546. + 310393.i 0.164787 + 0.503700i
\(786\) −1.37569e6 −2.22677
\(787\) 228223. + 228223.i 0.368477 + 0.368477i 0.866921 0.498445i \(-0.166095\pi\)
−0.498445 + 0.866921i \(0.666095\pi\)
\(788\) 94563.4 94563.4i 0.152290 0.152290i
\(789\) 1.44354e6i 2.31886i
\(790\) 1.44897e6 474037.i 2.32170 0.759553i
\(791\) −304845. −0.487221
\(792\) −1.90412e6 1.90412e6i −3.03559 3.03559i
\(793\) −113481. + 113481.i −0.180458 + 0.180458i
\(794\) 911896.i 1.44645i
\(795\) −150800. + 297446.i −0.238599 + 0.470624i
\(796\) 796702. 1.25739
\(797\) 703348. + 703348.i 1.10727 + 1.10727i 0.993508 + 0.113763i \(0.0362903\pi\)
0.113763 + 0.993508i \(0.463710\pi\)
\(798\) 567117. 567117.i 0.890568 0.890568i
\(799\) 453535.i 0.710423i
\(800\) 116025. 752208.i 0.181290 1.17532i
\(801\) −632140. −0.985255
\(802\) 722515. + 722515.i 1.12331 + 1.12331i
\(803\) −239604. + 239604.i −0.371589 + 0.371589i
\(804\) 4.62464e6i 7.15428i
\(805\) −123975. 62853.2i −0.191312 0.0969920i
\(806\) −351154. −0.540539
\(807\) −758297. 758297.i −1.16437 1.16437i
\(808\) 1.10323e6 1.10323e6i 1.68984 1.68984i
\(809\) 117237.i 0.179129i −0.995981 0.0895646i \(-0.971452\pi\)
0.995981 0.0895646i \(-0.0285476\pi\)
\(810\) 17059.8 + 52146.1i 0.0260018 + 0.0794788i
\(811\) −364516. −0.554210 −0.277105 0.960840i \(-0.589375\pi\)
−0.277105 + 0.960840i \(0.589375\pi\)
\(812\) −93705.5 93705.5i −0.142119 0.142119i
\(813\) 1.29354e6 1.29354e6i 1.95704 1.95704i
\(814\) 1.28941e6i 1.94599i
\(815\) −506260. + 165625.i −0.762182 + 0.249351i
\(816\) −1.50402e6 −2.25877
\(817\) 486176. + 486176.i 0.728365 + 0.728365i
\(818\) 186157. 186157.i 0.278211 0.278211i
\(819\) 123314.i 0.183842i
\(820\) −951032. + 1.87586e6i −1.41438 + 2.78980i
\(821\) −437621. −0.649249 −0.324625 0.945843i \(-0.605238\pi\)
−0.324625 + 0.945843i \(0.605238\pi\)
\(822\) −1.42334e6 1.42334e6i −2.10651 2.10651i
\(823\) −456640. + 456640.i −0.674178 + 0.674178i −0.958676 0.284498i \(-0.908173\pi\)
0.284498 + 0.958676i \(0.408173\pi\)
\(824\) 1.80147e6i 2.65321i
\(825\) −1.22711e6 189277.i −1.80292 0.278093i
\(826\) −308292. −0.451858
\(827\) −459888. 459888.i −0.672421 0.672421i 0.285853 0.958274i \(-0.407723\pi\)
−0.958274 + 0.285853i \(0.907723\pi\)
\(828\) 1.03082e6 1.03082e6i 1.50357 1.50357i
\(829\) 746352.i 1.08601i 0.839729 + 0.543006i \(0.182714\pi\)
−0.839729 + 0.543006i \(0.817286\pi\)
\(830\) −1.34796e6 683394.i −1.95668 0.992008i
\(831\) 914148. 1.32378
\(832\) 30983.1 + 30983.1i 0.0447588 + 0.0447588i
\(833\) −50170.2 + 50170.2i −0.0723029 + 0.0723029i
\(834\) 2.28373e6i 3.28331i
\(835\) −110501. 337764.i −0.158486 0.484440i
\(836\) −2.03104e6 −2.90607
\(837\) −515989. 515989.i −0.736529 0.736529i
\(838\) 697251. 697251.i 0.992891 0.992891i
\(839\) 1.11049e6i 1.57758i 0.614662 + 0.788791i \(0.289292\pi\)
−0.614662 + 0.788791i \(0.710708\pi\)
\(840\) 960550. 314248.i 1.36132 0.445363i
\(841\) 669038. 0.945929
\(842\) −248517. 248517.i −0.350535 0.350535i
\(843\) 1.53340e6 1.53340e6i 2.15775 2.15775i
\(844\) 2.75751e6i 3.87108i
\(845\) 294421. 580730.i 0.412340 0.813320i
\(846\) −2.11017e6 −2.94834
\(847\) 50095.4 + 50095.4i 0.0698283 + 0.0698283i
\(848\) −320903. + 320903.i −0.446254 + 0.446254i
\(849\) 647924.i 0.898894i
\(850\) −756264. + 554139.i −1.04673 + 0.766974i
\(851\) 392799. 0.542389
\(852\) 280043. + 280043.i 0.385785 + 0.385785i
\(853\) −444139. + 444139.i −0.610408 + 0.610408i −0.943052 0.332644i \(-0.892059\pi\)
0.332644 + 0.943052i \(0.392059\pi\)
\(854\) 429629.i 0.589085i
\(855\) 1.20883e6 + 612856.i 1.65361 + 0.838352i
\(856\) 1.52871e6 2.08630
\(857\) 609160. + 609160.i 0.829411 + 0.829411i 0.987435 0.158024i \(-0.0505125\pi\)
−0.158024 + 0.987435i \(0.550512\pi\)
\(858\) 511074. 511074.i 0.694239 0.694239i
\(859\) 291558.i 0.395129i −0.980290 0.197564i \(-0.936697\pi\)
0.980290 0.197564i \(-0.0633032\pi\)
\(860\) 478745. + 1.46336e6i 0.647302 + 1.97859i
\(861\) −622507. −0.839727
\(862\) 529858. + 529858.i 0.713091 + 0.713091i
\(863\) −161287. + 161287.i −0.216559 + 0.216559i −0.807047 0.590488i \(-0.798935\pi\)
0.590488 + 0.807047i \(0.298935\pi\)
\(864\) 920686.i 1.23334i
\(865\) 728472. 238322.i 0.973600 0.318517i
\(866\) −1.71236e6 −2.28327
\(867\) −421055. 421055.i −0.560145 0.560145i
\(868\) −462482. + 462482.i −0.613841 + 0.613841i
\(869\) 1.14272e6i 1.51322i
\(870\) 234373. 462288.i 0.309648 0.610764i
\(871\) 433754. 0.571752
\(872\) 1.27725e6 + 1.27725e6i 1.67975 + 1.67975i
\(873\) 91287.0 91287.0i 0.119779 0.119779i
\(874\) 889285.i 1.16417i
\(875\) 168671. 235139.i 0.220305 0.307120i
\(876\) 1.33381e6 1.73814
\(877\) −500503. 500503.i −0.650740 0.650740i 0.302431 0.953171i \(-0.402202\pi\)
−0.953171 + 0.302431i \(0.902202\pi\)
\(878\) 785524. 785524.i 1.01899 1.01899i
\(879\) 1.34781e6i 1.74443i
\(880\) −1.50704e6 764043.i −1.94607 0.986626i
\(881\) 1.05961e6 1.36519 0.682595 0.730797i \(-0.260851\pi\)
0.682595 + 0.730797i \(0.260851\pi\)
\(882\) 233428. + 233428.i 0.300065 + 0.300065i
\(883\) 864065. 864065.i 1.10822 1.10822i 0.114833 0.993385i \(-0.463367\pi\)
0.993385 0.114833i \(-0.0366332\pi\)
\(884\) 379719.i 0.485912i
\(885\) −260854. 797343.i −0.333051 1.01802i
\(886\) 1.98444e6 2.52796
\(887\) −224843. 224843.i −0.285780 0.285780i 0.549629 0.835409i \(-0.314769\pi\)
−0.835409 + 0.549629i \(0.814769\pi\)
\(888\) −2.01952e6 + 2.01952e6i −2.56108 + 2.56108i
\(889\) 325344.i 0.411661i
\(890\) −820726. + 268504.i −1.03614 + 0.338977i
\(891\) 41124.6 0.0518020
\(892\) −9976.10 9976.10i −0.0125381 0.0125381i
\(893\) −633288. + 633288.i −0.794142 + 0.794142i
\(894\) 2.44774e6i 3.06260i
\(895\) 205417. 405174.i 0.256442 0.505819i
\(896\) −243554. −0.303374
\(897\) 155691. + 155691.i 0.193499 + 0.193499i
\(898\) −1.01348e6 + 1.01348e6i −1.25680 + 1.25680i
\(899\) 188749.i 0.233542i
\(900\) 1.79384e6 + 2.44815e6i 2.21462 + 3.02241i
\(901\) 188751. 0.232509
\(902\) 1.60215e6 + 1.60215e6i 1.96920 + 1.96920i
\(903\) −322246. + 322246.i −0.395195 + 0.395195i
\(904\) 2.45768e6i 3.00738i
\(905\) 963197. + 488326.i 1.17603 + 0.596228i
\(906\) 3.98504e6 4.85486
\(907\) −763805. 763805.i −0.928470 0.928470i 0.0691372 0.997607i \(-0.477975\pi\)
−0.997607 + 0.0691372i \(0.977975\pi\)
\(908\) 522607. 522607.i 0.633875 0.633875i
\(909\) 1.38680e6i 1.67836i
\(910\) 52378.0 + 160102.i 0.0632508 + 0.193337i
\(911\) −36782.5 −0.0443205 −0.0221602 0.999754i \(-0.507054\pi\)
−0.0221602 + 0.999754i \(0.507054\pi\)
\(912\) 2.10012e6 + 2.10012e6i 2.52496 + 2.52496i
\(913\) −801006. + 801006.i −0.960936 + 0.960936i
\(914\) 1.15290e6i 1.38007i
\(915\) −1.11116e6 + 363521.i −1.32720 + 0.434197i
\(916\) −1.27112e6 −1.51493
\(917\) −169935. 169935.i −0.202090 0.202090i
\(918\) 801953. 801953.i 0.951620 0.951620i
\(919\) 1.21169e6i 1.43470i −0.696713 0.717350i \(-0.745355\pi\)
0.696713 0.717350i \(-0.254645\pi\)
\(920\) 506727. 999493.i 0.598685 1.18088i
\(921\) −1.39408e6 −1.64350
\(922\) 509107. + 509107.i 0.598890 + 0.598890i
\(923\) −26265.8 + 26265.8i −0.0308309 + 0.0308309i
\(924\) 1.34621e6i 1.57677i
\(925\) −124664. + 808212.i −0.145699 + 0.944586i
\(926\) −1.05158e6 −1.22637
\(927\) −1.13225e6 1.13225e6i −1.31760 1.31760i
\(928\) 168394. 168394.i 0.195538 0.195538i
\(929\) 526211.i 0.609718i 0.952398 + 0.304859i \(0.0986093\pi\)
−0.952398 + 0.304859i \(0.901391\pi\)
\(930\) −2.28162e6 1.15674e6i −2.63801 1.33743i
\(931\) 140109. 0.161647
\(932\) −449102. 449102.i −0.517026 0.517026i
\(933\) 91595.5 91595.5i 0.105223 0.105223i
\(934\) 2.72703e6i 3.12605i
\(935\) 218509. + 667908.i 0.249946 + 0.764001i
\(936\) −994166. −1.13477
\(937\) −762510. 762510.i −0.868493 0.868493i 0.123813 0.992306i \(-0.460488\pi\)
−0.992306 + 0.123813i \(0.960488\pi\)
\(938\) 821079. 821079.i 0.933209 0.933209i
\(939\) 2.16260e6i 2.45270i
\(940\) −1.90616e6 + 623608.i −2.15727 + 0.705759i
\(941\) −98666.8 −0.111427 −0.0557137 0.998447i \(-0.517743\pi\)
−0.0557137 + 0.998447i \(0.517743\pi\)
\(942\) −979274. 979274.i −1.10358 1.10358i
\(943\) −488071. + 488071.i −0.548857 + 0.548857i
\(944\) 1.14165e6i 1.28112i
\(945\) −158291. + 312221.i −0.177253 + 0.349621i
\(946\) 1.65873e6 1.85350
\(947\) 835870. + 835870.i 0.932049 + 0.932049i 0.997834 0.0657847i \(-0.0209551\pi\)
−0.0657847 + 0.997834i \(0.520955\pi\)
\(948\) −3.18061e6 + 3.18061e6i −3.53911 + 3.53911i
\(949\) 125100.i 0.138908i
\(950\) 1.82977e6 + 282235.i 2.02744 + 0.312726i
\(951\) 843930. 0.933137
\(952\) −404475. 404475.i −0.446291 0.446291i
\(953\) 992061. 992061.i 1.09233 1.09233i 0.0970474 0.995280i \(-0.469060\pi\)
0.995280 0.0970474i \(-0.0309398\pi\)
\(954\) 878206.i 0.964938i
\(955\) −510466. 258798.i −0.559707 0.283762i
\(956\) −3.47439e6 −3.80157
\(957\) −274708. 274708.i −0.299949 0.299949i
\(958\) 1.26230e6 1.26230e6i 1.37541 1.37541i
\(959\) 351642.i 0.382353i
\(960\) 99250.2 + 303375.i 0.107693 + 0.329182i
\(961\) 8048.05 0.00871453
\(962\) −336609. 336609.i −0.363727 0.363727i
\(963\) −960816. + 960816.i −1.03607 + 1.03607i
\(964\) 1.63054e6i 1.75460i
\(965\) 1.24458e6 407170.i 1.33650 0.437242i
\(966\) 589433. 0.631656
\(967\) 102132. + 102132.i 0.109221 + 0.109221i 0.759605 0.650384i \(-0.225392\pi\)
−0.650384 + 0.759605i \(0.725392\pi\)
\(968\) −403873. + 403873.i −0.431017 + 0.431017i
\(969\) 1.23526e6i 1.31556i
\(970\) 79746.1 157295.i 0.0847551 0.167175i
\(971\) −476996. −0.505913 −0.252957 0.967478i \(-0.581403\pi\)
−0.252957 + 0.967478i \(0.581403\pi\)
\(972\) 1.46997e6 + 1.46997e6i 1.55588 + 1.55588i
\(973\) −282103. + 282103.i −0.297977 + 0.297977i
\(974\) 486623.i 0.512949i
\(975\) −369758. + 270933.i −0.388963 + 0.285005i
\(976\) −1.59098e6 −1.67019
\(977\) −434620. 434620.i −0.455324 0.455324i 0.441793 0.897117i \(-0.354343\pi\)
−0.897117 + 0.441793i \(0.854343\pi\)
\(978\) 1.59723e6 1.59723e6i 1.66989 1.66989i
\(979\) 647260.i 0.675326i
\(980\) 279844. + 141877.i 0.291383 + 0.147727i
\(981\) −1.60555e6 −1.66834
\(982\) 707748. + 707748.i 0.733932 + 0.733932i
\(983\) −149156. + 149156.i −0.154359 + 0.154359i −0.780062 0.625702i \(-0.784812\pi\)
0.625702 + 0.780062i \(0.284812\pi\)
\(984\) 5.01869e6i 5.18323i
\(985\) 28411.6 + 86844.6i 0.0292835 + 0.0895097i
\(986\) −293355. −0.301744
\(987\) −419754. 419754.i −0.430884 0.430884i
\(988\) −530217. + 530217.i −0.543175 + 0.543175i
\(989\) 505307.i 0.516610i
\(990\) 3.10760e6 1.01666e6i 3.17069 1.03730i
\(991\) 116777. 0.118908 0.0594541 0.998231i \(-0.481064\pi\)
0.0594541 + 0.998231i \(0.481064\pi\)
\(992\) −831106. 831106.i −0.844565 0.844565i
\(993\) −150520. + 150520.i −0.152650 + 0.152650i
\(994\) 99440.0i 0.100644i
\(995\) −246151. + 485520.i −0.248631 + 0.490412i
\(996\) 4.45898e6 4.49487
\(997\) 363823. + 363823.i 0.366016 + 0.366016i 0.866022 0.500006i \(-0.166669\pi\)
−0.500006 + 0.866022i \(0.666669\pi\)
\(998\) 2.30897e6 2.30897e6i 2.31824 2.31824i
\(999\) 989234.i 0.991215i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 35.5.g.a.22.12 yes 24
5.2 odd 4 175.5.g.c.43.1 24
5.3 odd 4 inner 35.5.g.a.8.12 24
5.4 even 2 175.5.g.c.57.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.g.a.8.12 24 5.3 odd 4 inner
35.5.g.a.22.12 yes 24 1.1 even 1 trivial
175.5.g.c.43.1 24 5.2 odd 4
175.5.g.c.57.1 24 5.4 even 2